Hi there, I've been having trouble with 2 algebra questions, I was hoping someone here could give me a hand.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

(i) Consider the function R2 → R2 defined by f (x, y) = (3x − 4y, x − 2y). Let

v = (a, b) be the vector such that f (v) = (4, 6).

Find the vector v and hence calculate a + b.

(ii) Let f : R3 → R3 be a projection onto the xz-plane. Choose your favourite

basis E for R3 and calculate the matrix A of f with respect to E.

Calculate trace(A)

2. Relevant equations

N/A.

3. The attempt at a solution

(i) I am positive that this must be incorrect but i took that 3a - 4b =4 and a -2b = 6. Solving for a+b =-15.

(ii)I understand that the trace of a matrix is the sum of all the diagonal entries starting from the top left corner, but the phrasing question has left me clueless.

Any help would be greatly appreciated.

Thank you.

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# Homework Help: Finding a row vector and calculating the trace of a matrix

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